Privacy via ill-posedness

In this work, we exploit the ill-posedness of linear inverse
problems to design algoithms to release differentially private data or
measurements of the physical system. We discuss the spectral
requirements on a matrix such that only a small amount of noise is
needed to achieve privacy and contrast this with the poor conditioning
of the system. We then instantiate our framework with several
diffusion operators and explore recovery via l1 constrained
minimisation. Our work indicates that it is possible to produce
locally private sensor measurements that both keep the exact locations
of initial heat sources private and permit recovery of the “general
geographic vicinity” of the sources.

Joint work with Audra McMillan